Find the absolute maximum and the absolute minimum values of the following functions in the given intervals:

f(x) = 4x – x²/2 in [–2, 45]

given function is f(x) =

∴f'(x) = 4 – x

Now,

f'(x) = 0

4 – x = 0

x = 4

Then, we evaluate of f at critical points x = 4 and at the interval [ – 2, ]

f(4) = = 8

f(– 2) =

f() =

Hence, we can conclude that the absolute maximum value of f on [ – 2, 9/2] is 8 occurring at x = 4 and the absolute minimum value of f on [ – 2, 9/2] is – 10 occurring at x = – 2